Method and apparatus of tracking intersection line of curved surfaces performed by electronic device, and electronic device

Abstract

The method includes: generating a four-dimensional space parameter curve; dividing a parameter space corresponding to the first parametric surface into first surface boxes and a parameter space corresponding to the second parametric surface into second surface boxes; determining intersecting boxes among the first surface boxes and the second surface boxes as target boxes; constructing a tangent vector function model; establishing first and second determination conditions based on the tangent vector function model; marking target box satisfying the first determination condition as a first type box; marking target box satisfying the second determination condition as a second type box; marking target box other than the first type box and the second type box in the target boxes as a zeroth type box; generating tracking points in each type of box; and connecting the tracking points to generate an intersection line of the first parametric surface and the second parametric surface.

What is claimed is: 
     
         1 . A method of tracking an intersection line of curved surfaces performed by an electronic device, comprising:
 generating a four-dimensional space parameter curve associated with a first parametric curved surface and a second parametric curved surface according to a function model of the first parametric curved surface and a function model of the second parametric curved surface, and storing the four-dimensional space parameter curve in a register, based on a control instruction through an arithmetic unit, in response to the control instruction generated by a controller;   dividing a parameter space corresponding to the first parametric curved surface into a plurality of first curved surface boxes and dividing a parameter space corresponding to the second parametric curved surface into a plurality of second curved surface boxes so that intersecting boxes among the plurality of first curved surface boxes and the plurality of second curved surface boxes are determined as target boxes, and storing the target boxes in the register, based on the control instruction through the arithmetic unit;   reading the four-dimensional space parameter curve from the register, constructing a tangent vector function model for the four-dimensional space parameter curve, and storing the tangent vector function model in the register, based on the control instruction through the arithmetic unit;   reading the tangent vector function model from the register, and establishing a first determination condition and a second determination condition based on the tangent vector function model, based on the control instruction through the arithmetic unit, so that the target box satisfying the first determination condition is marked as a first type box, the target box satisfying the second determination condition is marked as a second type box, and the target box other than the first type box and the second type box in the target boxes is marked as a zeroth type box;   generating a plurality of tracking points in the first type box, the second type box and the zeroth type box respectively, and connecting the plurality of tracking points to generate an intersection line of the first parametric curved surface and the second parametric curved surface, based on the control instruction through the arithmetic unit; and   displaying the intersection line of the first parametric curved surface and the second parametric curved surface through a display unit.   
     
     
         2 . The method according to  claim 1 ,
 wherein the first parametric curved surface and the second parametric curved surface are parametric curved surfaces based on various types of curved surface entities and established according to a predetermined drawing scale, and the various types of curved surface entities at least comprise: a mechanical component curved surface entity, a human body part curved surface entity, and an animation object curved surface entity.   
     
     
         3 . The method according to  claim 1 , the establishing a first determination condition and a second determination condition based on the tangent vector function model comprises:
 inputting the target box into the tangent vector function model, outputting a target solution set, and storing the target solution set in the register, based on the control instruction through the arithmetic unit; and   reading the target solution set from the register, and establishing the first determination condition and the second determination condition by using the target solution set related to the tangent vector function model, based on the control instruction through the arithmetic unit.   
     
     
         4 . The method according to  claim 3 , wherein,
 the tangent vector function model comprises a first component vector function model, a second component vector function model, a third component vector function model, and a fourth component vector function model;   the target solution set output using the tangent vector function model comprises: a first solution set output through the first component vector function model, a second solution set output through the second component vector function model, a third solution set output through the third component vector function model, and a fourth solution set output through the fourth component vector function model;   the first determination condition is that: a zero solution exists in an intersection of the first solution set and the second solution set, or a zero solution exists in an intersection of the third solution set and the fourth solution set; and   the second determination condition is that: a zero solution exists at an intersection of the first solution set, the second solution set, the third solution set, and the fourth solution set.   
     
     
         5 . According to the method of  claim 4 , the generating a plurality of tracking points in the first type box, the second type box, and the zeroth type box respectively comprises:
 generating a plurality of different types of second tracking points for the second type box, wherein the different types of second tracking points at least comprises: a tangent point in a case that the first parametric curved surface and the second parametric curved surface are tangent to a point, a tangent point in a case that the first parametric curved surface and the second parametric curved surface are tangent to a curve, a tangent point in a case that the first parametric curved surface and the second parametric curved surface are coincident, a tangent point in a case that the first parametric curved surface and the second parametric curved surface are tangent to an isolated tangent point, and a tangent point in a case that the first parametric curved surface and the second parametric curved surface are tangent to a minimal loop;   generating a plurality of zeroth type tracking points by tracking the zeroth type box, wherein the zeroth type tracking point is a regular intersection point in a case that the first parametric curved surface or the second parametric curved surface is regularly intersected;   generating a plurality of different types of first tracking points for the first type box, wherein the plurality of different types of first tracking points at least comprises: a finite number of singular points existing on the first parametric curved surface or the second parametric curved surface, and a singular point on a singular curve existing on the first parametric curved surface or the second parametric curved surface; and   determining a third type box from the zeroth type box to generate a plurality of third tracking points for the third type box, wherein the third tracking point is a self-intersection point of the first parametric curved surface or the second parametric curved surface.   
     
     
         6 . The method according to  claim 5 , wherein the generating a plurality of different types of second tracking points for the second type box comprises:
 constructing a second discrimination function system according to the tangent vector function model and the four-dimensional space parameter curve; and   subdividing the second type box, according to a number of solutions of the second discrimination function system, to generate the plurality of different types of second tracking points according to the subdivided second type box.   
     
     
         7 . The method according to  claim 5 , wherein the generating a plurality of different types of first tracking points for the first type box comprises:
 constructing a sub function system for the first parametric curved surface or the second parametric curved surface;   constructing a first discrimination function system according to the sub function system and the four-dimensional space parameter curve; and   subdividing the first type box, according to a number of solutions of the first discrimination function system, to generate the plurality of different types of first tracking points according to the subdivided first type box.   
     
     
         8 . The method according to  claim 5 , wherein the determining a third type box from the zeroth type box comprises:
 establishing a third determination condition according to the tangent vector function model, wherein the third determination condition is that: at least one of a first sub condition, a second sub condition, a third sub condition, and a fourth sub condition is satisfied; the first sub condition is that: no zero solution exists in the first solution set and no zero solution exists in the third solution set; the second sub condition is that: no zero solution exists in the first solution set and no zero solution exists in the fourth solution set; the third sub condition is that: no zero solution exists in the second solution set and no zero solution exists in the third solution set; and the fourth sub condition is that: no zero solution exists in the second solution set and no zero solution exists in the fourth solution set; and   determining the zeroth type box satisfying the third determination condition as an exclusion box, and determining a box other than the exclusion box and a regular box in the zeroth type box as the third type box, wherein the regular box is a box corresponding to the zeroth type tracking point.   
     
     
         9 . An apparatus of tracking an intersection line of curved surfaces, comprising:
 a first generation module configured to, generate a four-dimensional space parameter curve associated with a first parametric curved surface and a second parametric curved surface according to a function model of the first parametric curved surface and a function model of the second parametric curved surface, and store the four-dimensional space parameter curve in a register, based on a control instruction through an arithmetic unit, in response to the control instruction generated by a controller;   a division module configured to divide a parameter space corresponding to the first parametric curved surface into a plurality of first curved surface boxes and divide a parameter space corresponding to the second parametric curved surface into a plurality of second curved surface boxes so that intersecting boxes among the plurality of first curved surface boxes and the plurality of second curved surface boxes are determined as target boxes, and storing the target boxes in the register, based on the control instruction through the arithmetic unit;   a construction module configured to read the four-dimensional space parameter curve from the register, construct a tangent vector function model for the four-dimensional space parameter curve, and store the tangent vector function model in the register, based on the control instruction through the arithmetic unit;   a marking module configured to read the tangent vector function model from the register, and establish a first determination condition and a second determination condition based on the tangent vector function model, based on the control instruction through the arithmetic unit, so that the target box satisfying the first determination condition is marked as a first type box, the target box satisfying the second determination condition is marked as a second type box, and the target box other than the first type box and the second type box in the target boxes is marked as a zeroth type box;   a second generation module configured to generate a plurality of tracking points in the first type box, the second type box, and the zeroth type box respectively, and connect the plurality of tracking points to generate an intersection line of the first parametric curved surface and the second parametric curved surface, based on the control instruction through the arithmetic unit; and   a display module configured to display the intersection line of the first parametric curved surface and the second parametric curved surface through a display unit.   
     
     
         10 . An electronic device, comprising:
 one or more processors; and   a storage apparatus configured to store one or more programs,   wherein the one or more programs, when executed by the one or more processors, cause the one or more processors to execute the method according to  claim 1 .